Spins Dynamics in a Dissipative Environment: Hierarchal Equations of Motion Approach Using a Graphics Processing Unit (GPU).

Abstract

A system with many energy states coupled to a harmonic oscillator bath is considered. To study quantum non-Markovian system-bath dynamics numerically rigorously and nonperturbatively, we developed a computer code for the reduced hierarchy equations of motion (HEOM) for a graphics processor unit (GPU) that can treat the system as large as 4096 energy states. The code employs a Padé spectrum decomposition (PSD) for a construction of HEOM and the exponential integrators. Dynamics of a quantum spin glass system are studied by calculating the free induction decay signal for the cases of 3 × 2 to 3 × 4 triangular lattices with antiferromagnetic interactions. We found that spins relax faster at lower temperature due to transitions through a quantum coherent state, as represented by the off-diagonal elements of the reduced density matrix, while it has been known that the spins relax slower due to suppression of thermal activation in a classical case. The decay of the spins are qualitatively similar regardless of the lattice sizes. The pathway of spin relaxation is analyzed under a sudden temperature drop condition. The Compute Unified Device Architecture (CUDA) based source code used in the present calculations is provided as Supporting Information .